Heat the olive oil in a large pot over medium heat and cook the onion for 7 minutes until golden. Add the garlic and cook 1 minute more.
Stir in the tomato paste and let it fry in the oil for 2 full minutes until it turns brick red. This deepens the flavor more than any other step in the recipe.
Add the canned tomatoes with their juice, crushing them with a spoon, along with the broth, sugar, salt, pepper, and red pepper flakes. Simmer uncovered for 25 minutes.
Blend the soup until completely smooth using an immersion blender, or in batches in a standing blender with the lid vented.
Stir in the coconut milk, fresh basil, and balsamic vinegar, then blend once more just until the basil disappears into the soup and it turns a deep creamy orange.
Butter one side of each bread slice with the dairy free butter and sprinkle the garlic powder over the cheddar shreds. Build two sandwiches with the buttered sides facing out.
Toast the sandwiches in a skillet over medium low heat for 4 minutes per side, pressing gently, until deep golden and the cheese has melted. Cut them into small cubes.
Ladle the soup into bowls and pile the warm grilled cheese croutons on top right before serving.